“What a small world indeed!” we say when discovering that a person we’ve just met used to study at our high-school, or has a relative that used to worked with us a few years ago. But just how small is it?

It was this question that drove Stanley Milgram and his colleagues back in 1967 to conduct what would be later called “Milgram’s experiment”. With the desire to understand the connections that form the basis of our communities, Miligram and his crew chose random individuals in the U.S. cities of Omaha, Nebraska and Wichita, Kansas and asked them to assist in forwarding a package to an individual in Boston, Massachusetts. This was done by either sending the package directly to the destination in case the sender knew the destination personally, or sending the package to some friend or relative of the sender who may be more likely to know the target personally (with the instructions required to continue the process from this point). When (and if) the package eventually reached the contact person in Boston, the researchers could track its exact course. What interest the researchers was to find out the probability that two randomly selected people would know each other, or alternatively – what is the “average shortest path” between any two random people. The results that were obtained by analyzing the paths of the packages that reached the target yielded an average path length of little less than 6 (which led to the coining of the phrase “six degrees of separation”, referring to the distance between any pair of people at the U.S).

An illustration of the Six Degrees of Separation model, from Wikipedia

This result was (still is) validated from time to time, hinting that almost everywhere, human population follows the “small world model”, as defined by :

Analyzing small world networks one can quickly notice a few of their distinctive properties. One example is the existence of many cliques and near-cliques (that is, clusters that contain a linking edge between every pair, or almost every pair, of nodes). Another interesting property is the fact that small world networks usually contain a great number of “hubs” (i.e. nodes with a high number of connections). Serving as “bridges” between many nodes, these hubs are in charge of the generation of short connecting paths that characterize these networks (for example, imagine “airport hubs” that are used by airlines in order to enable passengers to travel between each two cities using at most three flights).

But what can we learn from all this? And how can this benefit us when studying social trading? This will be discussed next week.